Eye of Cthulhu
HP: 2,800 (stage 1), 1,400 (stage 2)
Defense: 12 (stage 1), 0 (stage 2)
Attack Damage: 15 (stage 1), 0 (stage 2)
Special Abilities: Summons Servant of Cthulhus.
The Eye of Cthulhu is very easy to defeat, even with Copper Armor or, if one is skilled, no armor. Shurikens are your best bet in this fight. If you somehow managed to get your hands on Throwing Knifes or Poisoned Throwing Knifes, it would make the fight even easier. Another option would be to use a Bow (I'd advise you to use a Silver or Golden one), with Flaming Arrows (best results). Also, a Broadsword (Silver or Golden) would be useful for getting the Servants of Cthulhu off you if you're getting swarmed. Of course, a few Healing Potions would be helpful if you took too much damage.
I also recommand you to build an arena that is 27 (height) times 30 (length) with Wooden Platforms for even 6 blocks high. There should be 4 floors, and the remaining three blocks are designed to prevent you from being knocked out of the arena and injured/killed by the fall.
In the first stage, the EoW will fire Servants of Cthulhu (around 3-6) at you, while hovering high above your reach, and you should spam Shurikens at the EoC's lens, where the SoC spawns. After that the EoC will charge at you, which would be the perfect time to use the Bow w/ Flaming Arrows to deal some good damage. After a few charges the EoC will fly back up again and attempt to barrage you with SoCs again. Alternate back to Shurikens and do the same again. For each cycle, I'd expect the player to deal around 100 - 200 damage. Repeating this for a few times and the EoC's HP should be down to 1,400 pretty fast.
The EoC will spin and shed its lens to set the fight into the second stage. The EoC will now fly close enough to the player so that its melee attacks are more accurate and deadly. However it is also defenseless now so you can bombard it with Shurikens or Flaming Arrows to do lots of damage. Just be mobile though, since its attacks are now much more dangerous.
There are some tips that you could use to fight the EoC. First is that, when it transforms, it takes 3 seconds to do that. Make them useful and do whatever you can to damage it extensivey. Another is that, despite the EoC being fast, it can't turn as quickly. That can give the player a huge advantage since you can simply run in one direction, letting the EoC follow you, then rapidly changing direction to confuse it, attacking it while you do so.
After it dies, it drops some Demonite Ore, which you could craft into War Ax of the Night (I strongly recommand that), and the Ax would come in handy if you want to fight the Eater of Worlds next.
Eater of Worlds
HP: 65 (head), 150 (body segment), 220 (tail), 7,785 (added up - 1 head, 50 segments and 1 tail, may vary)
Defense: 0 (head), 2 (body segments), 4 (tail)
Attack Damage: 40 (head), 15 (body segments), 10 (tail)
Special Abilities: Splits into multiple sections to swarm the player.
The EoW is harder than EoC, but is still a piece of cake, provided if you take good percautions. Like the EoC, the EoW should best be fought in a arena, though the difference is that the arena is best if its in the air (6 blocks up the air would be great). This is because the EoW burrows underground and it's hard to tell when or where it will emerge next time. Hunter Potions negate that problem however, but the arena is still recommanded.
Since the Eater of Worlds can split, turning into many segments, I'd advise you not to focus too much damage into just one area, but across the entire monster. If you've beaten the Goblin Army (I did), Spiky Balls and Harpoon are two fantastic chories. The Spiky Balls can be placed across the arena before summoning and can rapidly damage the entire EoW intensely, which is great, and I used that tactic to defeat the EoW twice in quick succession. The Harpoon, for it to have equal effectiveness, is best used at melee range. Since the Harpoon retracts instantly after hitting something, its rate of fire increases if the object you hit is close. In fact, it can have a fire rate of a Minishark at close range (effectively becoming a Imitation Megashark due to its high damage output).
If you haven't defeated the Goblin Army yet, don't worry. If you have the arena, previously mentioned weapons like Shurikens or Throwing Knifes still work, but not as effective as Vilethorn, if you got one by smashing Shadow Orbs. The Ball o' Hurt is also a great choice, since you can hold the mouse to let the flail to stay in one place so all of the EoW's segments will pass through the flail, effectively making a meat grinder. The War Ax of the Night also works nice too, due to its high damage.
There's a weakness the EoW has, which is its tendency to stall and stop a bit after a segment is destroyed. Using a War Ax of Night in conjunction with Shadow Armor (increases melee speed), you can deal enough damage quickly to kill the second head that newly spawned (it will sort of hesitate when it morphs from a segment into a head), since the head only has 65 HP. Also, firing the Vilethorn at the direction that the EoW is coming would be the most effective.
HP: 4,400 (head), 600 (hands), 5600 (summed up)
Defense: 6 (head), 9 (hands)
Damage: 35 (head), 32 (hands)
Special Abilities: (Nothing more than a massive floating skull w/ two hands)
Skeletron is noticably harder than the EoC and EoW, mainly because he's much more mobile and damaging. First of all, due to its high HP and defense, Shurikens and Throwing Knife wouldn't be as useful. And now it's time to bring in more damaging weapons. The Demon Bow w/ Flaming, Unholy or Jester's Arrows, a Blade of Grass (or Fiery Greatsword, if you somehow managed to survive long enough in Underworld before you even went in the Dungeon). Of course, the Ball o' Hurt and the Harpoon are two nice and effective weapons against it. Minishark is good (though a massive amount of bullets are required), and so is Star Cannon (if you can afford the stars).
Keep in mind to always attempt to avoid the hands, which is Skeletron's main weapon. You can choose to either destroy Skeletron's hands (they have only 600 health and should be easily disposed of) to render Skeletron almost useless, or you can simply aim all your attacks at the skull, since if the skull dies the hands die with it.
Like the previous two bosses, it's best to fight Skeletron on a smooth surface, since a large obstable would mean massacre upon the player. I'd also note that Skeletron will always stay on the upper half of the screen (so does Skeletron Prime), so that you can just fight him on a normal ground surface (it's good to put a 7 block high blockage to prevent other stuffs like Zombies from harassing you).
A good tip is, Skeletron might sometimes roll his head rapidly while moving towards (and follows) you at the same time. During this period his defense drops to 0, and you can use some high-damage weapons to devastate Skeletron. Another is, don't melee. Skeletron will only swat his hands at you, or clapping them togather to crush you. Just spam your best ranged weapons at it and you'll be fine.
Wall of Flesh
HP: 8,000 (wall), 240 (Hungries), 60 (Leeches)
Defense: 12 (mouth), 0 (eyes)
Attack: 50 (melee), laser damage depends on the wall's HP.
The Wall of Flesh is quite difficult. I died many times myself, too. From personal bitter experiences, it's almost nessecary to build a bridge, or simply scouting the farther regions in Underworld, since you won't want a obsidian house to block your way as you're fighting it. An important note is that, if you're facing left side while dropping the doll, the wall will ALWAYS appear on the right side and push towards the left side, since it will be disastrous if you built a bridge, threw the doll in the lava at one side and the wall spawns on the opposite side of your bridge.
Although this sounds wierd, but Meteor Armor with Space Gun is actually incredibly effective. Use an Ironskin Potion to compansate for the defense loss. Since it has unlimited ammo and fast rate of fire, it has an impressive DPS. However some say that Phoenix Blaster and Minishark works better. This is entirely your choice. For the quickest (but most expensive) way, is to use a Star Cannon. A very important note is that you shouldn't aim for the mouth, but you should go for the eyes, because they have no defense. Also, you can use grenades to clear out Hungries when the wall first spawns. Open fire on the wall after all Hungries are dead. Since the hungries will detach and fly at you, use some long range sword (Fiery Greatsword, Blade of Grass, Nights Edge, and so on) to get rid of them for good.
And one last tip is that you can use a grappling hook to rapidly travel away from the wall if its too close. Or a Swiftness Potion can let you outrun the wall.
Hey thank you all for watching. If you disagree with some things I wrote, feel free to comment below! (as long as people don't use vulgar or offensive terms). Also if you want more tips and infos just consult the admins, their knowledge is much wider than me. :P